Boxless, you are correct. That is the way I do my arbors and extensions. Also why the test shaft is still sitting in the lathe three days later.
I will drill, bore and ream 1/2" hole, 1-3/4 deep in a collet or chuck. Then flip and rough out the other side. Take to mill , drill & tap two set screws to tighten on motor shaft. Now I go back top lathe and clamp piece of round stock in and turn 1/2" shaft 1-1/2" as perfect as possible, no taper. I want an air tight sliding fit. Slide the arbor on and take very light cuts to dimension and threading. Center drill and tap screw hole. Done. If I don't screw up, everything will read almost 0, usually does.
It is extra work but beats even a collet for concentrically.